Humankind has been on a quest to find some kind of immortality for as long as we've been truly human in our evolution. We've never reached the kind of immortality that's the stuff of mythology, but we might find ourselves surprisingly close due to technology. The progression of our quest for that immortality looks something like this:

Likeness Immortality
Being able to have your picture drawn or your likeness sculpted. Since prehistoric times.

Idea Immortality
Being able to record your ideas and thoughts on paper. Since the beginning of recorded history.

Photographic Immortality
Having your exact likeness recorded in a photograph. Since the 1800s.

Digital Immortality
Having your experiences recorded digitally and stored on connected networks like the Internet. Since the 1990s or thereabouts.

Animatronic Immortality
Having a personality engine built upon your thoughts, ideas, and knowledge. Forthcoming. Not as far-fetched as the idea sounds on the surface, since to a large extent we are our habits, and our decision-making processes can be mimicked pretty accurately with logic ladders and other tools that can be programmed into binary computing languages.

Bionic Immortality
Having your brain preserved even after the "expiration date" of your body. Forthcoming. Will require some brave early adopters to try crossing the brain/computer barrier, but some people are already experiencing it with enhancements like cochlear implants and now brain-stem implants. We still don't know quite enough about how the brain works to be able to "download" what a person knows, but as we figure out more and more, we'll find ways of making something like that happen. There will be brave souls -- perhaps some with nothing to lose, who face terminal diseases -- who will volunteer to try to cross that gap so that their minds can survive after their bodies fail. At the same time, the rapid development of bionics and even lab-grown organs should allow us to replace body parts and organs as they wear out, much like we would replace worn parts in a machine. That technology is already being demonstrated with replicated organs in rats. Staving off physical failure with medical engineering will become a pursuit on a grand scale.